The average concentration of ${\mathrm{SO}}_2$ in the atmosphere over a city on a certain day is $10 \mathrm{ppm},$ when the average temperature is $298 \mathrm{K}$. Given that the solubility of ${\mathrm{SO}}_2$ in water at $298 \mathrm{K}$ is $1.3653 \raisebox{1ex}{$\mathrm{mol}$}\!\left/ \!\raisebox{-1ex}{$\mathrm{L}$}\right.$ and the ${\mathrm{pK}}_{\mathrm{a}}$ of ${\mathrm{H}}_2{\mathrm{SO}}_3$ is $1.92,$ estimate the $\mathrm{pH}$ of rain on that day.

Calculate the pressure exerted $\left(\text{in} \mathrm{atm}\right)$ by one mole of ${\mathrm{CO}}_2$ gas at $273 \mathrm{K}$ if the Van der Waal's constant $\mathrm{a}=3.593 {\mathrm{dm}}^6 \mathrm{atm} {\mathrm{mol}}^{-2}.$ Assume that the volume occupied by ${\mathrm{CO}}_2$ molecules is negligible. Answer correct up to two places of decimal.

The figures given below show the location of atoms in three crystallographic planes in an $\mathrm{FCC}$ lattice. Draw the unit cell for the corresponding structure and identify these planes in your diagram.

A hydrogenation reaction is carried out at $500 \mathrm{K}$. If the same reaction is carried out in the presence of a catalyst at the same rate, the temperature required is $400 \mathrm{K}$. Calculate the activation energy of the reaction in $\frac{\mathrm{kJ}}{\mathrm{mol}}$ if the catalyst lowers the activation barrier by $20 \frac{\mathrm{kJ}}{\mathrm{mol}}$.

Write integer as the answer.

Copper sulphate solution $(250 \mathrm{mL})$ was electrolysed using a platinum anode and copper cathode. A constant current of $2 \mathrm{mA}$ was passed for $16 \mathrm{minutes}$. It was found that after electrolysis the absorbance of the solution was reduced to $50\%$ of its original value. Calculate the concentration of copper sulphate in the solution to begin with.

If the answer is of type $\mathrm{y}\times {10}^{-5} \mathrm{M}$, report the value of $\mathrm{y}$ correct up to three places of decimal.

Calculate the energy required to excite $1 \mathrm{litre}$ of ${\mathrm{H}}_2$ gas at $1 \mathrm{atm}$ and $298 \mathrm{K}$ to the first excited state of atomic hydrogen. The energy for the dissociation of $\mathrm{H}-\mathrm{H}$ bonds is $436 \frac{\mathrm{kJ}}{\mathrm{mol}}$. Rydberg constant for $\mathrm{H}=109679 {\mathrm{cm}}^{-1}, \mathrm{h}=6.626\times {10}^{-34} \mathrm{Js}$ and $\mathrm{C}=3\times {10}^8 \frac{\mathrm{m}}{\mathrm{s}}$.

A sample of argon gas at $1 \mathrm{atm}$pressure and $27 °\mathrm{C}$ expands reversibly and adiabatically from $1.25 {\mathrm{dm}}^3$ to $2.50 {\mathrm{dm}}^3.$ Calculate the enthalpy change in this process (in J). ${\mathrm{C}}_{\mathrm{V}, \mathrm{m}}$ for argon is $12.48 {\mathrm{JK}}^{-1} {\mathrm{mol}}^{-1}$.

To $500 {\mathrm{cm}}^3$ of water, $3\times {10}^{-3} \mathrm{kg}$ of acetic acid is added. If $23\%$ of acetic acid is dissociated, what will be the depression in freezing point? ${\mathrm{K}}_{\mathrm{f}}$ and density of water are $1.86 \mathrm{K} {\mathrm{kg}}^{-1} {\mathrm{mol}}^{-1}$ and $0.997 \mathrm{g} {\mathrm{cm}}^{-3}$ respectively.

Give answer after multiplying with 100 and rounding off to the nearest integer value.

Show that the reaction $\mathrm{CO}\left(\mathrm{g}\right)+\frac{1}{2}{\mathrm{O}}_2\left(\mathrm{g}\right)\to {\mathrm{CO}}_2\left(\mathrm{g}\right)$ at $300 \mathrm{K}$ is spontaneous and exothermic, when the standard entropy change is $-0.094 \mathrm{kJ} {\mathrm{mol}}^{-1}{\mathrm{K}}^{-1}.$ The standard Gibbs free energies of formation for ${\mathrm{CO}}_2$ and $\mathrm{CO}$ are $-394.4$and $-137.2 \mathrm{kJ} {\mathrm{mol}}^{-1}$ respectively.